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Dresden Database Research Group 14

\dfrac{\dfrac{1}{6}}{4} = \frac{1}{24}

-48^{1/2} + 75^{1/2} = -(16\cdot 3)^{1/2} + (25\cdot 3)^{1/2}

\frac{49 (-1) - 21 q}{-12 q + 28 (-1)} = \frac147 \frac{1}{7(-1) - q*3}(-3q + 7(-1))

6*(-1) + 22.5 = 16.5

0.637 = 1 - 0.3627 \cdot \dotsm

\tfrac12 = \frac{1}{1 - -1}

\frac{1/4 \cdot 4}{(m + 1) \cdot (m + 9)} = \frac{1}{4 \cdot (9 + m) \cdot (m + 1)} \cdot 4

|w + \left(-1\right)| + |x + (-1)| = |w| + |x| = |w + 1| + |x + 1|

\sin(\dfrac{4\cdot \pi}{3}) = -\sin(\pi/3)

{360\over120} = 3

-\frac{1}{\left(2\times (-1) + m\right)^2} = \frac{\mathrm{d}}{\mathrm{d}m} \dfrac{1}{m + 2\times (-1)}

5 + (\dfrac{40}{5}) = 5 + (8) = 5 + 8 = 13

\mathbb{E}\left(G \times v\right) = G \times G \times v = G \times v = G \times v

5^{\frac{1}{2}}\cdot (4\cdot (-1) + 5) = 5^{\frac{1}{2}}

\left(B_2*3 - \frac{3}{2} + 1 = 0 \implies B_2*3 = 1/2\right) \implies B_2 = 1/6

\overline{F \cup \overline{H}} = H \cap \overline{F} = H \backslash F

c \cdot b = b/c = b \cdot c^7

\frac149 - \frac{5}{12} = \frac{9*3}{4*3} - \dfrac{5}{12}1 = 27/12 - 5/12 = \frac{1}{12}(27 + 5(-1)) = \dfrac{22}{12}

(y + x)^2 = x \cdot x + 2xy + y^2

2 \cdot l! = 2 \cdot 1 \cdot 2 \cdot \cdots \cdot l = 2 \cdot 4 \cdot \cdots \cdot 2 \cdot l

(-a)^{2k} = (-1)^{2k} a^{2k} = 1^k a^{2k} = a^{2k}

x_m + h_m = x_m + h_m

2/3 \cdot \left(-4/7\right) = \frac{\frac17 \cdot (-4)}{3 \cdot \frac{1}{2}}

\frac{π}{2} + \frac{1}{2}*π = π

4\cdot a\cdot 4\cdot a\cdot 1/2 = 8\cdot a^2

2^{1 / 2} \approx 1.41\cdot \dots < 1.44 = 1.2 \cdot 1.2 = (5/4) \cdot (5/4)

5! = 5\times 4\times 3\times 2

\left(2 + a = |a \cdot 2 - i \cdot a| \Rightarrow 2 + 5^{\frac{1}{2}} \cdot a + a = 0\right) \Rightarrow a = -\frac{2}{5^{\frac{1}{2}} + 1}

\mathbb{E}(V) \cdot \mathbb{E}(X) = \mathbb{E}(X \cdot V)

\frac{-25 + i*20}{5 - 4i} = \frac{-25 + i*20}{5 - 4i} \dfrac{1}{5 + 4i}(5 + i*4)

\mathbb{E}\left(b\right)\cdot \mathbb{E}\left(f\right) = \mathbb{E}\left(b\cdot f\right) = 0 \implies 0 = b\cdot f

x^2 - x + 2\cdot \left(-1\right) = (1 + x)\cdot (x + 2\cdot \left(-1\right))

2\cdot \pi\cdot r^3 = \dfrac23\cdot \pi\cdot R^3 \Rightarrow r = \frac{1}{3^{\frac13}}\cdot R

12 + 10 \cdot (-1) = 2

\frac{1}{-q*7 + 4}*(-q*7 + 4)*(-\frac{5}{6}) = \frac{1}{-42*q + 24}*\left(35*q + 20*(-1)\right)

2*x + 2 + 3 = 5 + x*2

24 - 24*(-1) + 47 = 24*2 + 47*(-1)

97 = 0 \cdot 5! + 4! \cdot 4 + 0 \cdot 3! + 0 \cdot 2! + 0 \cdot 1! + 0!

\frac12 \cdot (a + b) = \dfrac{1}{2} \cdot (a + b)

m^3 \leq m^3\times 2 + 5\times (-1) \Rightarrow m^3 \geq 5

\frac{1}{2009} + 2/2008*\frac{2008}{2009} = 3/2009

\frac{\text{d}}{\text{d}a} \tan^{-1}{a} = \dfrac{1}{1 + a^2}

a^4\cdot x = x = a^3\cdot x

0\cdot 0\cdot 0\cdot 0\cdot 0 = 0^5

-\frac{4}{1 + x^2\cdot 16} = -4 + 64\cdot x^2 - 1024\cdot x^4 + x^6\cdot 16384 - \ldots

x - h - h + e - 2x = -h \cdot 2 + x \cdot 3 - e

x^{m\cdot 5} + x + 1 + x^{5\cdot m + 3} - x^{m\cdot 5} = x^{3 + m\cdot 5} + x + 1

0 > z \implies |z| = -z

-\frac{4}{2} + 4/2 + \frac{1}{4} \cdot 18 = \dfrac{9}{2}

2 \cdot (2 \cdot a^2 + a \cdot 2 + 37) = 73 + (2 \cdot a + 1)^2

\dfrac{38}{7} = \frac{1}{14}*(21 + 30 + 10 + 12 + 3)

\binom{2 + 4}{4} = \binom{6}{2}

\left(\left(z^2 - y^2\right)^2 + \left(2\cdot z\cdot y\right)^2\right)^{1/2} = \left((z^2 + y^2)^2\right)^{1/2} = z^2 + y \cdot y

\frac{1}{6 + 10}\cdot 32 = 32/16 = 32/16 = 2

(-1) + 2*x = x^2 - (1 - x)^2

\tfrac{1}{12} \cdot 29 \cdot \pi = 3/4 \cdot \pi + \tfrac{5}{3} \cdot \pi

-z\cdot \tan{a} + \tan(c + a)\cdot z = y \Rightarrow z = \dfrac{y}{\tan(a + c) - \tan{a}}

13 \cdot x = 4 + x \cdot 5 + x \cdot 8 + 4 \cdot (-1)

10 - 9 \cdot (-6) = 10 + 54 = 64

2*f - f + 1 = 2*f - f + (-1) = f + (-1)

\cos{y} = \cos{\frac{y}{2} \cdot 2}

\frac{9}{x^2}\cdot 1/5 = \frac{9}{5\cdot x^2}

0.83\cdot 0.689 = 0.83\cdot 0.83\cdot 0.83 = 0.83^3

x_{l*2} = -1/(2*l) rightarrow \lim_{l \to \infty} x_{2*l} = 0

\tfrac{\frac{1}{36}*7}{\frac14} = \frac79

x/\pi \cdot \pi = x

\|\varphi_1 + \cdots + \varphi_l + \varphi_{l + 1}\| = \|\varphi_1 + \cdots + \varphi_l + \varphi_{l + 1}\|

0\cdot \cot(0) = 0 = 0

\left|{x}\right| = \left|{Z}\right| \cdot \frac{\left|{x}\right|}{\left|{Z}\right|} = \left|{Z}\right| \cdot \left|{x}\right| \cdot \left|{1/Z}\right| = \left|{Z \cdot x/Z}\right|

(q + (-1))\cdot ((-1) + p) = p\cdot q - p - q + 1

(dr)^3 = 3375 \implies 15 = dr

\frac{5^{\tfrac{1}{5}} + (5 \cdot 5)^{1/5} + ... + (5^n)^{\frac15}}{\frac{1}{5^{1/5}} + \frac{...}{\left(5^2\right)^{\frac{1}{5}}} + \dfrac{1}{\left(5^n\right)^{\frac{1}{5}}}} = \dfrac{(5^{n + 1})^{\frac{1}{5}}}{\dfrac{1}{5^{1/5}} + \frac{...}{(5^2)^{1/5}} + \frac{1}{(5^n)^{\frac{1}{5}}}}\cdot (\frac{1}{5^{1/5}} + \frac{...}{(5 \cdot 5)^{1/5}} + \frac{1}{(5^n)^{1/5}}) = (5^{n + 1})^{1/5}

1^3 = 1^2\Longrightarrow 3 = 2

6 \cdot \sqrt{34} + 35 = \frac{6 + \sqrt{34}}{-\sqrt{34} + 6}

73 = (214\cdot (-1) + 360)/2

0 = h^l = h^{l + 2 \cdot (-1)} \cdot h^2 = h^{l + 2 \cdot \left(-1\right)} \cdot h = h^{l + (-1)}

h^2 - g \times g = (g + h)\times (h - g)

4 \cdot l^2 \cdot m^2 - l \cdot l \cdot m^2 \cdot 2 = m^2 \cdot l^2 \cdot 2

(z \cdot z - \sqrt{2}) \cdot \left(\sqrt{2} + z^2\right) = z^4 + 2 \cdot (-1)

-9/2 \cdot \frac{1}{\left(-1\right) - 9 \cdot \mu} \cdot \left(-\mu \cdot 9 + \left(-1\right)\right) = \tfrac{81 \cdot \mu + 9}{2 \cdot (-1) - 18 \cdot \mu}

1.6^{\left(-1\right) + n} = 1.6 \times 1.6^{n + 2 \times \left(-1\right)}

(2*(-1) + p)*(6 + p) = p^2 + 4*p + 12*\left(-1\right)

x^{b + d} = x^b\times x^d

\sqrt{7}\cdot 8 = (4 + 5 + (-1)) \sqrt{7}

x^{1/2} = (-\left(-1\right) \cdot x)^{1/2} = i \cdot (-x)^{1/2}

x^3 - y^3 + x - y = (x - y)*(1 + x^2 + x*y + y^2)

\left((-10.6)\cdot 1/(-5)\right)/(-0.4) = -\frac{1}{(-5)\cdot (-0.4)}\cdot 10.6 = -10.6/2

2*(-1) + (\frac1x + x) * (\frac1x + x) = x * x + \frac{1}{x^2}

\dfrac{2}{100} + \frac{1}{100}*70 = 2/100 + 7/10

\sin\left(E_1 + E_2\right) = \cos(E_2) \cdot \sin\left(E_1\right) + \cos(E_1) \cdot \sin(E_2)

-5/3*\pi + \pi*17/12 = -\frac{\pi}{4}

1/\left(C_2\right) - \tfrac{1}{C_1} = \frac{C_1 - C_2}{C_1 \cdot C_2}

(e^{\frac13 \cdot 5 \cdot \pi \cdot i})^{15} = e^{\dfrac{5}{3} \cdot i \cdot \pi \cdot 15}

-16 = 0 \cdot 4 + 3 \cdot (-2) + 5 \cdot (-2)

\cos(\arctan{\zeta}) = \frac{1}{(\zeta^2 + 1)^{\frac{1}{2}}}

g^2 - f \cdot f = \left(g + f\right) \cdot (g - f)

-2\cdot y = 6\cdot e^{(-5 - 2\cdot y)/2} = 6\cdot \frac{1}{e^{5/2}}\cdot e^{-y}

D \cdot 3 + 2 - 2 \cdot D + 2 \cdot \left(-1\right) = D

\frac{\sin(z)}{\frac{1}{\cos(z)}}\tfrac{1}{\cos(z)} = \frac{\tan(z)}{\sec(z)}

\frac{\pi}{2} - \pi/4 = \dfrac14 \cdot \pi